Question

In the adjoining figure, find the perimeter of the shaded region where $ADC$, $AEB$ and $BFC$ are semi-circle on diameter $AC$, $AB$ and $BC$ respectively.

Answer 1

Given:

Diameter of semicircle $AEB=2.8cm$

radius of semicircle $\left(AEB\right)=\frac{28}{2}=1.4cm$

Diameter of semicircle $BFC=1.4cm$

radius of semicircle $\left(BEC\right)=\frac{1.4}{2}$

Diameter of semicircle $ADC=2.8+1.4=4.2cm$

radius of semicircle $\left(ADC\right)=4.212=2.1cm$

perimeter of shaded region = and sum of arc of semicircle $AEB$,

$BFC$and $ADC=[(\pi \times 1.4)+(\pi \times 0.7)+(\pi \times 2.1)]cm$

$=\pi (1.4+0.7+2.1)cm$

$=\left(\frac{22}{7}\right)\times .4$

$=22\times .6$

$=13.2cm$

Perimeter of shaded region is $13.2cm$